EECS 461: Probability and Statistics
Daily Schedule
  Spring 2008



Schedule:
Lecture period: TR 1:00-2:15, 202 Robinson Center


Instructor: Prof. Erik Perrins
Office: 2044 Eaton Hall
Office hours: TR 9:15-10:30 and 2:15-3:30. Drop-ins at other times are always welcome but
are best scheduled via e-mail.
Office phone: 864-7370/864-7770
E-mail: esp "at" eecs.ku.edu

 Text: Probability: An Introduction with Statistical Applications, by J. Kinney, 1997.

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  HW is assigned on the dates shown.  It is due at the beginning of the next lecture period.


Day
 Date
 Quiz/Exam
 Reading Assignment
 HW Set
 HW Due Next Lecture
Thur
 01/17
Sec. 1.1-1.3
 1
 1.1.9, 1.1.11
Tues
 01/22
Sec. 1.3, 1.4
 2
 1.3.1, 1.3.7, 1.4.3, 1.4.12
Thur
 01/24
Sec. 1.5, 1.6
 3
 1.5.5, 1.5.7, 1.6.1, 1.6.2
Tues
 01/29
Sec. 1.6, 1.7
 4
 1.7.14, 1.7.15
Thur
 01/31
Sec. 2.1-2.3
 5
 2.2.3, 2.2.11
Tues
 02/05
 SQ #1
 Sec. 2.3-2.4
 6
 2.3.1, 2.3.6
Thur
 02/07
Sec. 2.4-2.6
 7
 2.5.15, 2.5.16, 2.6.5
Tues
 02/12
Sec. 2.7-2.9
 8
 2.7.7, 2.9.8, 2.9.13
Thur
 02/14
Sec. 2.10-2.12
 9
 2.10.2
Tues
 02/19
Sec. 2.13, 2.14
 10
 Supp. Exer. 2.20, 2.14.14, 2.14.19
Thur
 02/21
SNOW DAY, no class

Tues
 02/26
 SQ #2
 Sec. 3.1-3.3 11
 3.1.4, 3.1.14, 3.2.5, and C1
Thur
 02/28
Sec. 3.4, 3.5 12
 3.2.9, 3.4.1, 3.4.3
Tues
 03/04
Sec. 3.5
 13
 3.4.9, 3.4.13, 3.5.6, 3.5.25
Thur
 03/06
Sec. 3.6-3.8
 14
 3.6.12, 3.6.13
Tues
 03/11
[Review]
Expectation Problems (due date 4/22)
Thur
 03/13
 Midterm

C2



SPRING BREAK

Tues
 03/25
Sec. 4.1-4.3
 15
 4.3.1, 4.3.3, 4.3.9, 4.3.14
Thur
 03/27
Sec. 4.4-4.7
 16
 4.4.5, 4.5.7
Tues
 04/01
Sec. 4.8-4.10
 17
 4.7.3, 4.8.4
Thur
 04/03
Sec. 4.11, 4.12
 18
 4.11.1, 4.11.15
Tues
 04/08
ROCK CHALK JAYHAWK!

Thur
 04/10
Sec. 4.13, 4.14 19 4.13.1, 4.13.5
Tues
 04/15
Sec. 4.15
 20
 4.14.1, 4.14.15, C3
Thur
 04/17
Sec. 4.16
 21
 4.15.2, 4.15.15, 4.16.7
Tues
 04/22
Sec. 5.1, 5.2

Thur
 04/24
 SQ#3
 Sec. 5.2
 22
 5.2.6, 5.2.13, 5.2.14, C4
Tues
 04/29
Sec. 5.3-5.5
 23
 5.3.1, 5.3.10
Thur
 05/01
Sec. 5.6
 24
 5.5.4, 5.5.12, 5.5.16, C5
Tues
 05/06
Sec. 5.7
 25
 5.7.1, 5.7.3
Thur
 05/08
COURSE REVIEW


The final exam is scheduled for Monday, May 12, from 1:30-4:00.


C1 [Due 03/04]
Generate n pseudo-random uniformly distributed numbers on the interval (0,1), plot the (bar graph) frequency histogram (10 cells), and then plot the stair-step cumulative distribution function as a line graph (not as a bar graph) for (a) n=100 and (b) n=900.  For both graphs, insert proper abscissa values (0.1,...).

C2 [Due 04/03]
Work Problem 3.4.8 in Kinney's book.

C3 [Due 04/22]
Generate 1200 uniform random numbers X on (0,1).  Form a sample value of a random variable Z by summing the first 12 samples of X and subtracting the number 6.0, and so forth to yield 100 samples of Z.  Plot the histogram and cumulative distribution for Z. (This exercise demonstrates the  Central Limit Theorem.)

C4 [Due 05/01]
Generate 100 sample values each of X and Y as independent uniform random variables on (0,1).  Form W and Z from the Box-Muller formulas given by:
         W = sqrt(-2.0*ln(X))*cos(2*pi*Y)
         Z = sqrt(-2.0*ln(X))*sin(2*pi*Y)
Plot histograms (100 points each, 10 cells) and cumulative distribution functions for W and Z.

C5 [Due 05/08]
In C3 and C4 you generated three data sets, with 100 sample values in each set (Z in C3, and W and Z in C4).  Compute the sample mean and sample variance for each data set (in other words, crunch each data set down to a sample mean and sample variance).  We already suspect that each of these random variables (Z, W, and Z) has zero mean and unit variance.  Now we will test these hypotheses.  Based on your sample means and variances, form 95% confidence intervals for the means and variances of Z (in C3) and W and Z (in C4).  Using a null hypothesis that the mean is zero and the variance is one, calculate p values for all three cases and compare these to the 5% level of significance, identifying whether the hypotheses are accepted or rejected.


Answers to Even-Numbered Problems:

1.4.12: 9/44
1.6.2: 2p2 - p4
1.7.14: 27/95
2.3.6: mean=121/81, var=4556/6561
2.5.16: 120
2.9.8: a) 0.4722, b) 1/16
2.10.2: 28/435
Supp. Exer. 2.20: a) 0.3528, b) 116
3.1.4: a) 4/5, b) 2/75
3.1.14: 1/5
3.5.6:  a) 0.1056, b) 0.01
3.6.12: a) 3/10, b) 0.3483, c) 0.0296195 (with binomial) and 0.02887 (with normal approx)
4.3.14: a) 1/3, b) 1/3
4.8.4: lambda/(lambda - t)
4.15.2: a) t7 = -2.13 (accept Ho), b) z = -2.04 (reject Ho), c) F(7,9) = 0.12, T11 = -0.9738 (accept Ho)
5.2.6: b) 12x(1-x)2, 0 < x < 1, 12y(1-y)2, 0 < y < 1, c) 43/256
5.2.14: b) 0.25*ln(2)
5.3.10: a) k=10, b) f(x) = 10x/3(1-x3), g(y) = 5y4, c) 3y2/(1-x3)
5.5.12: not independent
5.5.16: 1/2